a cylinder , a cone and a hemisphere of equal base have the same height what is their ratio - Maths - Surface Areas and Volumes

Question

a cylinder , a cone and a hemisphere of equal base have the same
height what is their ratio in their volumes ?

Lalit Mehra · Accepted Answer

Let r and h be the radius of base and height of the cylinder, cone and hemisphere.

We know that, Height of hemisphere = Radius of the hemisphere

∴ h = r

Volume of cylinder = πr²h = πr² × r = πr³

Volume of cone = $\frac{1}{3} π r^{2} h = \frac{1}{3} π r^{2} \times r = \frac{1}{3} π r^{3}$

Volume of hemisphere = $\frac{2}{3} π r^{3}$

Volume of cylinder : Volume of cone : Volume of hemisphere

$= π r^{3} : \frac{1}{3} π r^{3} : \frac{2}{3} π r^{3} = 1 : \frac{1}{3} : \frac{2}{3} (Dividing by π r^{3}) = 3 : 1 : 2 (Multiplying by 3)$

Thus, the ratio of their volumes is 3 : 1 : 2.

a cylinder , a cone and a hemisphere of equal base have the same height. what is their ratio in their volumes ?